Problem: Simplify. Rewrite the expression in the form $b^n$. $\dfrac{b^{10}}{b^6}=$
Solution: $\begin{aligned} \dfrac{b^{10}}{b^6}&=b^{10-6} \\\\ &=b^4 \end{aligned}$ This follows from the general rule $\dfrac{x^m}{x^n}=x^{m-n}$. Note that the powers have the same base. We can also see this is correct by expanding the powers. $\begin{aligned} \dfrac{b^{10}}{b^6}&=\dfrac{\overbrace{\cancel b\cdot \cancel b\cdot \cancel b\cdot \cancel b\cdot \cancel b\cdot \cancel b\cdot b\cdot b\cdot b\cdot b}^\text{10 times}}{\underbrace{\cancel b\cdot \cancel b\cdot \cancel b\cdot \cancel b\cdot \cancel b\cdot \cancel b}_\text{6 times}} \\\\\\ &=\underbrace{b\cdot b\cdot b\cdot b}_\text{4 times} \\\\ &=b^4 \end{aligned}$ In conclusion, $\dfrac{b^{10}}{b^6}=b^4$.